TY - JOUR

T1 - Real-Space Renormalization Estimates for Two-Phase Flow in Porous Media

AU - Hansen, Alex

AU - Roux, Stéphane

AU - Aharony, Amnon

AU - Feder, Jens

AU - Jøssang, Torstein

AU - Hardy, H. H.

PY - 1997

Y1 - 1997

N2 - We present a spatial renormalization group algorithm to handle immiscible two-phase flow in heterogeneous porous media. We call this algorithm FRACTAM-R, where FRACTAM is an acronym for Fast Renormalization Algorithm for Correlated Transport in Anisotropic Media, and the R stands for relative permeability. Originally, FRACTAM was an approximate iterative process that replaces the L x L lattice of grid blocks, representing the reservoir, by a (L/2) x (L/2) one. In fact, FRACTAM replaces the original L x L lattice by a hierarchical (fractal) lattice, in such a way that finding the solution of the two-phase flow equations becomes trivial. This triviality translates in practice into computer efficiency. For N = L x L grid blocks we find that the computer time necessary to calculate fractional flow F(t) and pressure P(t) as a function of time scales as τ ∼ N1.7 for FRACTAM-R. This should be contrasted with the computational time of a conventional grid simulator τ ∼ N2.3. The solution we find in this way is an acurate approximation to the direct solution of the original problem.

AB - We present a spatial renormalization group algorithm to handle immiscible two-phase flow in heterogeneous porous media. We call this algorithm FRACTAM-R, where FRACTAM is an acronym for Fast Renormalization Algorithm for Correlated Transport in Anisotropic Media, and the R stands for relative permeability. Originally, FRACTAM was an approximate iterative process that replaces the L x L lattice of grid blocks, representing the reservoir, by a (L/2) x (L/2) one. In fact, FRACTAM replaces the original L x L lattice by a hierarchical (fractal) lattice, in such a way that finding the solution of the two-phase flow equations becomes trivial. This triviality translates in practice into computer efficiency. For N = L x L grid blocks we find that the computer time necessary to calculate fractional flow F(t) and pressure P(t) as a function of time scales as τ ∼ N1.7 for FRACTAM-R. This should be contrasted with the computational time of a conventional grid simulator τ ∼ N2.3. The solution we find in this way is an acurate approximation to the direct solution of the original problem.

KW - Effective properties

KW - Heterogeneity

KW - Relative permeability

KW - Renormalization numerical algorithm

KW - Simulation

UR - http://www.scopus.com/inward/record.url?scp=0031430142&partnerID=8YFLogxK

U2 - 10.1023/A:1006593820928

DO - 10.1023/A:1006593820928

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0031430142

SN - 0169-3913

VL - 29

SP - 247

EP - 279

JO - Transport in Porous Media

JF - Transport in Porous Media

IS - 3

ER -